Automation System for Single Photon Generation and Detection

Single photon source can be produced by using spontaneous parametric down conversion or quantum emitter such as ions, molecules, atoms, quantum dots and colour centres. Main objective of current research is to automate single photon generation module and detection module based on nitrogen vacancy colour centre in diamond into one system. In single photon generation, diamond sample is held at a holder mounted on a 3D piezo translation stage. Laser source with wavelength 527nm is focused using a standard microscope objective to a spot size at the nitrogen vacancy centre to produce fluorescence. Since a single photon is generated by exciting an isolated nitrogen vacancy in a diamond crystal, it is critical that position of nitrogen vacancies in the crystal to be known. For this purpose, a scanning system was designed and constructed to determine the 3D position of nitrogen vacancy and identified their coordinates for later use. The system consists of a high precision 3D piezo translation stage and was controlled by a scanning programme built using LabVIEW. This programme will map the location of the vacancies in an intensity graph where axis X and Y show the scanning position while the bright colour spots determine the position of the vacancies. In single photon detection which is based on the Hanbury-Brown-Twiss setup, the fluorescence emitted from the nitrogen vacancy is split by a beamsplitter and directed to single photon detectors. A digital pulse is produced for each photocount detected. At the same time, output from the detectors is fed into a time to amplitude converter/single channel analyzer to produce coincidence counts. In order to read and record the number of photon counts and number of coincidences, a detection system was designed and built. This detection system interfaces a series of high performance single photon detectors to the same computer that controls the scanning system via a detection programme. Besides reading and recording data, the detection programme can also calculate the second order correlation function, g2(τ) from a subVI written in LabVIEW 8.2

Computation of quantum bound states on a singly punctured two-torus

We study a quantum mechanical system on a singly punctured two-torus with bound states described by the Maass waveforms which are eigenfunctions of the hyperbolic Laplace—Beltrami operator. Since the discrete eigenvalues of the Maass cusp form are not known analytically, they are solved numerically using an adapted algorithm of Hejhal and Then to compute Maass cusp forms on the punctured two-torus. We report on the computational results of the lower lying eigenvalues for the punctured two-torus and find that they are doubly-degenerate. We also visualize the eigenstates of selected eigenvalues using GridMathematica

Study of simple pendulum using tracker video analysis and high speed camera: an interactive approach to analyze oscillatory motion

In this paper, we report on the use of Tracker video analysis and high speed camera as an interactive approach to study oscillatory motion of a simple pendulum. Tracker software is basically a computer based learning tool and is preferred because it is free, user friendly and support effective learning and teaching. Combining with the high speed camera that records the motion of pendulum at a frame rate up to 1000 frames per second (fps), analysis of the motion is performed at different angles and video qualities. The periods obtained from the experiment are then compared with the exact period expression and Lima and Arun approximation in order to determine how well this approach suited for the large angle approximation. Results have shown that when the video qualities improved, errors are minimal but errors increased when the angle increased. This research finding shows that this approach is feasible in studying the motion of simple pendulum and at the same time, interactive and inexpensive

Numerical method for computing Maass cusp forms on triply punctured two-sphere

A quantum mechanical system on a punctured surface modeled on hyperbolic space has always been an important subject of research in mathematics and physics. This corresponding quantum system is governed by the Schrödinger equation whose solutions are the Maass waveforms. Spectral studies on these Maass waveforms are known to contain both continuous and discrete eigenvalues. The discrete eigenfunctions are usually called the Maass Cusp Forms (MCF) where their discrete eigenvalues are not known analytically. We introduce a numerical method based on Hejhal and Then algorithm using GridMathematica for computing MCF on a punctured surface with three cusps namely the triply punctured two-sphere. We also report on a pullback algorithm for the punctured surface and a point locater algorithm to facilitate the complete pullback which are essential parts of the main algorithm

Computing Maass cusp form on general hyperbolic torus

The bound states of a quantum mechanical system on a punctured hyperbolic torus are described by Maass cusp forms, which are eigenfunctions of the hyperbolic Laplace-Beltrami operator vanishing at infinity. In a recent work by Chan et al. (2013), the computation of Maass cusp forms makes use of the symmetric fundamental domain for the hyperbolic torus. As a result, the Maass cusp forms then are divided into odd and even classes. It is of interest to consider the case when no symmetry is assumed. This requires the expansion of Maass cusp form in its complex Fourier form. In this paper, we show the available algorithm can be extended to employ directly the complex Fourier expansion using Mathematica. We were able to reproduce the results of Chan et al, on the symmetric hyperbolic torus but now with the capability of applying the algorithm even for the case of asymmetric hyperbolic torus

Effects of step-potential on confinement strength of strain-induced type-I core–shell quantum dots

In this paper, the transition energy between lowest unoccupied molecular orbital (LUMO) of conduction band and highest occupied molecular orbital (HOMO) of valence band for band structures of type-I core-shell quantum dots (CSQDs) within a strong and weak confinements of charge carriers are estimated using the effective mass approximation together with single-band model. The effect of potential step at the conduction and valence bands on the confinement strength is then properly discussed. Our numerical results show that for a same size of CSQDs, the one with bigger potential steps will have stronger carriers' confinement with more localized excitons

Physical, structural and optical properties of erbium doped rice husk silicate borotellurite (Er-doped RHSBT) glasses

A series of erbium doped rice husk silicate borotellurite glasses with chemical composition {[(TeO2)0.7 (B2O3)0.3]0.8 (SiO2)0.2}1 − x (Er2O3)x with x = 0.01, 0.02, 0.03, 0.04 and 0.05 mol was prepared using the melt-quenching technique. The density and the molar volume were determined and found to be increasing with Er3 + concentration. The glasses were subjected to FTIR and XRD to study the structural changes in the glass. UV–Vis spectroscopy was carried out to obtain the absorption spectrum that is used in the calculation of the optical energy band gap (Direct and Indirect), the Urbach energy and the refractive index. Using the refractive index, density and molar volume, the molar polarizability, metallization criterion, polaron radius, average boron‑boron separation, inter-nuclear distance of Er3 +, surface reflection loss, transmission coefficient and oxygen packing density were determined. The density, molar volume, optical band gaps, molar refraction, transmission coefficient and metallization criterion were found to have increased with increasing concentration of Er3 + ions. While the values of the refractive index, Urbach energy and inter-nuclear distance of Er3 + ions decreased. As more Er3 + ions were introduced, the reflectivity of the glasses decreased. The polaron radius also decreased, with the values suggesting that the glass has small polaron

Polarizability, optical basicity and electric susceptibility of Er3+ doped silicate borotellurite glasses

Glasses system was fabricated using the chemical composition {[(TeO2)0.7 (B2O3)0.3]0.8 (SiO2)0.2}1 − x (Er2O3)x with x = 0.01, 0.02, 0.03, 0.04 and 0.05 by melt-quenching method. The glasses were subjected to FTIR and XRD to study the glass structural changes and amorphous nature respectively. The absorption spectrum of the glasses were obtained from UV–Vis spectroscopy and used to calculate the energy band gap. Using the Archimedes principle, the density and the molar volume were determined. From the density, molar volume, and energy band gap, other parameters such as refractive index, molar refractive index, metallization criterion, reflection loss, transmission coefficient, polarizability, optical basicity, polaron radius, dielectric constant, optical dielectric constant, electric susceptibility, average electronegativity and others parameters were obtained by calculation. The polarizability values and the optical basicity were found to increase with Er3 + ions concentration increase. The dielectric constant, optical dielectric constant and the linear electric susceptibility decreased with increase in Er3 + ions concentration. The properties studied for the erbium doped glass system suggest the glass system has a potential in the EDFA application

Higher-order singular value decomposition and the reduced density matrices of three qubits

In this paper, we demonstrate that higher order singular value decomposition (HOSVD) can be used to identify special states in three qubits by local unitary (LU) operations. Since the matrix unfoldings of three qubits are related to their reduced density matrices, HOSVD simultaneously diagonalizes the one-body reduced density matrices of three qubits. From the all-orthogonality conditions of HOSVD, we computed the special states of three qubits. Furthermore, we showed that it is possible to construct a polytope that encapsulates all the special states of three qubits by LU operations with HOSVD